Pick up the steed in the same location as for the mounted daily quest, then run to the opposite side of the keep to the north, just north of the profession trainers. Talk to the Squire, let the summoned combatant come to you, then run away and start the fight. It's fairly easy.

If you fail, you will be knocked of your horse. Mount a new one (there is one nearby) and talk to the Squire again to re-try the test.

After completing "The Valiant's Challenge", the following quests open up allowing players to repeat the valiant stage of daily quests (steps six and seven) for the other factions with which they have not yet earned the right to champion: